A vehicle, such as an automobile, uses an electric power steering apparatus which applies steering assist torque to a steering mechanism including front wheels, by driving an electric motor in accordance with steering torque applied by a driver (or crew) operating a steering wheel. In such an electric power steering apparatus, as disclosed in a patent document 1, phase compensation (i.e. damping control) is performed on a target value of a base assist current, which is supplied to the electric motor in accordance with the applied steering assist torque. By virtue of this structure, a damping component can be considered, which allows the convergence of the steering to be improved.    Patent Document 1: Japanese Patent Application Laid Open No. 2004-203112